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Science and Math For Adults?
Peter Trepan writes "Like most Americans, I made it through high-school and college without a thorough understanding of major scientific and mathematical concepts. I'm trying to remedy this situation both for personal betterment and so I can supplement my *own* kids' education. The problem is, most textbooks are not designed to convey an understanding of the subject, but to squeeze in all the 'facts' required by state law. I'm looking for books that don't just tell me an equation or a concept works, but also explain *why*. Would you please list books that have helped you gain a greater understanding of the basic concepts of algebra, chemistry, calculus, physics, and other core areas of science?" This is similar to an earlier question, but with a broader focus.
Feynman has 6 easy/not so easy peices on physics... I enjoyed those. On A whole I will recomend any of his books... Math I'm not sure... I'd like to try and find a math book (that teaches you as much as a text book) thats not as dry as one... For calculus for the easy stuff Learn Calculus the easy way is a interesting concept, its taught through a story.
zero, the biography of a dangerous idea by charles seife (sp?)
the god particle, by leon lederman
the particle garden, by someone whose name i can't remember.
good math and good physics. enjoy!
-Leigh
Stephen Hawking's "Universe in a Nutshell" is a good start on physics and relativity. I've never taken any physics and was able to understand it fairly well.
Calculus Made Easy by Silvanus P. Thompson and Martin Gardner. This is exactly the sort of book you're looking for, in the subject of Calculus. To quote from the preface, on the subject of modern math textbooks: Their exercises have, as one mathematician recently put it, "the dignity of solving crossword puzzles." The purpose of this book is to explain the philosophy of Calculus, and teach you how to differentiate and integrate simple functions. I recommend reading the Preface in a bookstore, skimming the first few chapters. I think you'll like it.
I'm as mimsy as the next borogove but your mome raths are completely outgrabe.
One article that I found interesting A Guide to Infinity
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Any of his non-fiction books, and there's a ton. All subjects, from algebra to the brain to chemistry. (He even wrote about the Bible...)
They say the first thing to go is your penis. Well, it's either that or your brain. I forget which...
You might check out some of the materials on display at ArsDigita University, they have lectures online and a critique of each course, together with a list of texts...personally, Sispser's text for Theory of Computation was very helpful in explaining a lot of the higher-level CS Math.
The solution that most math texts take then is to give you *lots* of problems/drills so that the mechanics get ingrained, allowing the insight to come later.
When I screwed up my second year calculus course *really* badly (like 6% on the midterm...) I used a Schaum's Outline to get back on track (and eventually ace the final). It's main benefit is *heaps* of problems to work through. That made me a convert to the problems approach to math teaching.
The key is to do all the problems, in order.
That said, I can't really recommend one math text over another, just so long as there are lots of problems, and hopefully a solution key in the back for at least half the excercises.
"Foudations of Mathematics" by Denbow and Goedicke (old, but an amazing book for the understanding of most math concepts) "Mathematical Sorcery" by Clawson (More of a "evolution of modern math concepts")
There are "for Dummies" books that cover many of the topics you've listed. I was never fond of them, but you may want to take a look at them.
The biggest problem when you're undertaking a self-study endeavour is that most books that are available are either
- Very specialized topics (What does pi mean?)
- Refresher-course books (Lots of problems, few explanations)
The specialized topics books - commonly reviewed in magazines such as Scientific American - are fun to read, but I'm not sure if they serve the purpose of what you're seeking.
How much of algebra do you know? If you can look through the table of contents of a textbook for Algebra I and II and are confident in all the topics, then I'd move on to geometry/trigonometry before calculus.
Also, keep in mind that conceptual physics texts are divided between algebra-based and calculus-based reasoning. Take whichever you're more comfortable with.
Some 'refresher-course' books that will come in handy with the conceptual books that others may suggest:
Schaum's Outlines
Research & Education Association's Problem Solvers series
CliffsNotes and SparkNotes
The problem is, most textbooks are designed to be companion references, with all the 'facts' squeezed in so the teacher can spend time helping everyone understand the concepts etc. The two work together.
Simple answer is, you need to take adult education classes. I left college barely half-way through, and ended up taking night classes- intro to calculus was one; another was an intensive Economics class. I found them worthwhile; I probably would have enjoyed the class more if I wasn't young enough to be most of the other student's kid(you would fit in FAR better, from the sounds of it.)
Without the classes, you don't get the benefits of peer learning, in-class interaction("Did everybody get that?" [blank stares] "Heh, ok, let me explain it a different way...") the discipline that testing creates, nor the resource of having a Really Smart Person(professor) to go to when you need help. There are also other benefits- making friends(you're probably all in similar 'boats' so to speak, so people socialize pretty readily), and networking. My old boss decided to do part-time classes for an MBA, and got a lot of networking out of it(granted, those were business classes, more prone to networking activities, but you get the idea).
Please help metamoderate.
...and very little from the books.
I suppose it depends on the type of learner you are, but frankly, I imagine seeing and using the information being delivered to me. Rather than simply "knowing" the things I learned, I understood them and used what I learned to add more peices to the puzzle I call "reality."
In more simple terms, everything you (should have) learned should be assimilated into the way you operate within your environment. Ever heard "you use it or you lose it"? There's a lot of truth to that.
Rather than try to get what you missed from books, perhaps it's time to make a much more grand display by going back to school. It doesn't have to be thought of as "remedial" but rather as a "brush-up" or simply continuing education. If you show your children that learning only ends when you die, their minds will be open for life with the expectation that they can grow and improve themselves at any point in their lives... not just during the beginning phases. By the time they reach it, "middle aged" will be 50-something anyway.
Best advice? Go back to school and pay attention this time.
The math program I was a part of in high school, at Whitney Young Magnet School in Chicago, was called IMP, or Integrated Mathematics program but it could have just as easily stood for Interactive Mathematics Program.
Basically the way it was structured was that instead of the traditional math program where one learns algebra the first year, geometry the second, trig the third and then moves onto precal, we learned a litte bit of each every year.
Furthermore, instead of them just shoving facts down our throat and saying here, memorize these (such as all the proofs from traditional geometry) we were actually guided along in discovering them for ourselves.
Every problem was given to us in word problem format. Each unit, which represented a major concept such as the quadratic equation or some of that other stuff, was presented as one big word problemm and it was broken up into smaller pieces which slowly led up to the solution of the actual problem.
So instead of coming out of it with simply memorizing the quadratic equation, pythagorean theorem, pi, geometric proofs and the like, we were actually able to discover these on our own.
It's just too bad the teachers weren't all that great and the program didn't much fit into the "flash/bang" you need to know this information right now that most high school classes are based around. God forbid students actually understand and can apply the information they are learning.
I also can't seem to recall who published the books we used but I'm sure a bit of googling can solve that.
Douglas Hofstadter won a pulitzer for this little gem. This is a fantastic book to read for anyone remotely interested in the mathematical principles behind some of the more glamorous aspects of computing. Hofstadter's "Achilles & the Tortoise" dialogues are a frequently hilarious tribute to Lewis Carol that remain some of my most favorite things in print.
If you're lacking a basic understanding of algebra then this book may be a tad over your head, but if you can get into it you will find it immensely rewarding.
P.S. Algebra? ALGEBRA?!!?? You made it through college without algebra?
Real math involves proofs. In fact, for mathematicians that is the definition of mathematics. The rest is "just" application. Since the original poster is complaining about the lack of explanation why, I suggest that he look into proofs and other creative aspects of real mathmatics. If you haven't learned that math is a creative art you haven't learned jack. Ok, so I'm opinionated, but this is slashdot and what else is new.
Anyway I suggest that anybody of any age interested in math check out equations and wff-n-proof from the wff-n-proof people.
Regarding books, he had a vague request so I'll make some vague suggestions. Springer Verlag publishes lots of great mathbooks, as well as quite a few not so great. Some of them I can even read, and they do have a some series and books advertised for undergraduates. Look for yellow in any self respecting University library or technical bookstore.
Actually, going through a university library or bookstore is probably the best advice I can give under the teach a man to fish philosophy. Learning to go through a stack and pick out books that are readable but challenging is basically the secret to scholarhood. That and faith in the fact that once you've ground through one the rest will be a smidgen easier.
Oh, and you can also check out the math section of Cononical Tomes I made a few contributions when it first started, and would assume that it has only grown.
On the topic of calculus, don't learn anything past calculus I (well, bits of calculus II are useful). The rest is completely useless and you'll forget about it all in a couple of years anyway because of its uselessness. If you want something that's useful go for discrete math and/or the good bits of linear algebra. Your comment is completely offbase. Actually, Linear Algebra is about as important as Calculus in many scientific/engineering disciplines.
More importantly, you claim that anything more advanced will be forgotten, but the later courses often serve to reinforce earlier material. For example a course on Fourrier theory reinforces both Linear Algebra and Calculus.
Most math departments have a course somewhere after the introductory sequence which teaches basic proof techniques often by studying the definition of numerical systems from logical axioms.
These basic proof techniques are the very basis of mathematics. The reason so many people get through high school with little understanding of math is that they are never forced to do any proofs outside of Geometry.
In short, if you cannot prove anything, you know practically nothing about mathematics.
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People go to community college to transfer into a good university and get cheap credits, not get an education.
If they wanted me to focus on an education perhaps they wouldnt make the GPA so damn important.
What is the point of avoiding difficult but important classes simply to preserve your GPA? Are you in school to get an education or to simply achieve some arbitrary GPA? I've been in the position of hiring people for technical positions and I've always been far more impressed by a mediocre GPA in a substantial curriculum then a high GPA in an easy curriculum.
Ok say I do take a few math classes and get a few Cs, well then my GPA goes under 3.0 and I can forget about transfering into a good 4 year university, I can also forget about scholarships and grants which also require a high GPA of above 3.0 or 3.5, I really cannot afford any Cs and I know for a fact that its simply impossible for me to get an A or B in math. I take classes which I know I can/will get an A or B in.
This isnt about the jobs, this is about getting a degree from an elite private university.
I recently returned to school myself, so I do have sympathy with amount of work required to do really well in a course, and I do understand that those planning to continue to a four year school or go on to graduate school need to match minimum requirements, but in my opinion you'll be better served by reducing the number of classes you take in a given term then by trying to ditch the challenging courses.
I never take more than 4 classes per semester, and I never get anything below a B in grades, those are the rules I follow.
Maybe if universities werent so strict and competitive on the GPA issue I could actually focus on learning but right now I have a goal, that goal is to get into Harvard, Tufts, Boston College,Boston University or North Eastern, all which are ELITE private universities which will NOT let you in with a sub 3.0 GPA, you most likely wont get in with a sub 3.5 GPA, so no its not about "learning" right now, its about moving up the ladder, it will be about learning once I get into university, thats when I'll take math clases, get a C or two, and learn something.
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I confess that I made it through 3 semesters of college calculus and an engineering degree pretty much not understanding the underlying concepts of calculus. It's surprising what you can accomplish by rote. This book was a real forehead-slapper for me, and I can't recommend it highly enough. Many years after graduating, I've finally learned what I should have back then. If it were up to me, this would be the first book anyone learning calculus ever read. I wish Sylvanus Thompson were still alive (I think Calculus Made Easy was published in 1919) so I could give him a big smooch.
Calculus is INCREDIBLY important, and from a philosopical point of view it might even be dangerous. :)
Imagine a field of mathematics that explicitly has at it's underpinnings the hypothesis that as you break up a line into smaller segments, eventually if you make each segment have no length, they still all add up to a lenght.
Philosopy aside, it's an INCREDIBLE tool for particular applications. Need the area of a sphere, no problem. A cone, still no problem. An oddly shaped object that looks like a art-deco running shoe? BIG problem, that is unless you use calculus.
Physics: The Human Adventure, Gerald Holton and Stephen Brush
Nice, historical look at how well known physical concepts of today were discovered.
Physics for Scientists and Engineers, Paul Fishbane and Stephen Gasiorowicz
First few chapters good if you have a basic knowledge of calculus. For the later chapters (ie, Electricity and Magnetism, basic quantum mechanics) good idea to have a calculus book handy, I reccomend
Calculus: Early Transcendentals, James Stewart
First chapter is a good review of algebra, precalculus, and analytical geometry. Through chapter 7, fairly straightforward. Chapter on sequences and series is kind of fuzzy, though it mostly makes sense.
Hope this helps!
#define CLUE 0
For a literate and entertaining look at the concepts of calculus, I highly recommend David Berlinski's A Tour of the Calculus. It won't teach you how to solve problems, but it will teach you the concepts behind limits, differentiation, and integration along with the important theorems and their proofs.
The best piece of advice I can give anyone trying to learn from a textbook is to tell them to work through the problems. Anyone should be able to pick up many of the textbooks listed below and work though as many of the problems as time allows (limited either by patience or by real life events). Most textbooks provide answers to selected problems, so you can check your progress.
Absolutely, 100%. Nobody is born with the ability to take a triple scalar product or multiply two matrices (both happening in your video card when you're playing Doom!). As a great Calculus teacher once announced to his class through a thick French Canadian accent, "Math is not a spectator sport." (Actually, it came out as "Matt ees not a spectator sport.")
Having said that, Calculus is my favorite kind of math. It's incredibly elegant and probably the most useful advanced math, as it touches everything you do. Consider your car. If you calculate your speed using a watch and the odometer, you have an idea how fast you were going, but your speedometer is actually showing you the value of the derivative at any instantaneous time. Your speedometer shows the rate of change of position (distance travelled) at any instantaneous time. That's calculus.
Don't be afraid. "Calculus" (besides being a formal term for tartar the dentist scrapes off your teeth) means small stones in Latin... small stones as used for counting.
Two *great* books on the subject:
Remember: Do the problems, succeed. Don't do the problems, fail. It's that simple.
Fire and Meat. Yummy.
How. I understand the area under a graph is the intergral of the formula of the graph, but if you have an everyday shape, chances are its not created by a known mathematical formula. how do you work out the area using calculus?
Ahh... Now we discover the joy of Infinite Series. Infinite series allows you to do all sorts of things to (arbitrary) precision. (Arbitrary in that it won't spit back an answer to 300 decimal places unless you make the program you write run through the loop 300 times...)
Basically, here's the idea. You can do a regression of the known points on the graph to come up with a function (formula) to describe the relationship. Regressions come from infinite series, but are used in a plug-and-play format in statistics courses. Also annoyingly, Excel 95 and up includes the capability to do them in the Data Analysis tools, OpenOffice does not yet [grumble grumble]. Anyway, once you have a function, you simply integrate it to find the area.
My favorite part of all this is that the series usually gives you a nice long sum of little polynomial expressions, which are individually and collectively easy to integrate.
Practical applications? Fourier Transforms and Fast Fourier Transforms. They allow you to express any function (audio waveform?) as a sum of different overlapping sinewaves. From there, you can do all the math you want on them. MP3 and Ogg codecs do this.
Fire and Meat. Yummy.